DOUBLE-DIFFUSIVE FINGERING CONVECTION IN A POROUS-MEDIUM

We consider nonlinear two-dimensional, horizontally periodic, double-diffusive fingering convection in a saturated porous medium. The Darcy equation, including Brinkman and Forchheimer terms to account for viscous and inertia effects, respectively, is used for the momentum equation. A mixed Galerkin-finite difference method (Galerkin in the horizontal direction, finite difference in the vertical direction) is developed to solve the initial boundary value problem. Different values of the stabilizing temperature gradient, characterized by a thermal Rayleigh number R(T), ranging between 1 and 50 are considered. The stability boundaries which separate regions of different type of convective motion are identified in terms of R(T) and R(S), the solute Rayleigh number. For R(T) = 1, for instance, the steady convective flow which bifurcates from the motionless conduction solution at R(S)1 = 4pi2 + 1 persists in the face of small disturbances up to at least R(S) = 10R(S)1. At approximately R(S)2 = 440, a transition to time-periodic convection occurs. For a larger stabilizing temperature gradient (R(T) = 50), the steady-convective motion is stable with respect to small disturbances for R(S)1 = 4pi2 + 50 < R(S) < 4R(S)1. At approximately R(S)2 = 405, a periodic convection occurs and persists up to R(S)3 = 440, at which a multipeaked periodic solution is found.